Republican National Committee Chairman Reince Priebus said there was a consensus in the GOP for “serious immigration reform” in an interview with Politico about the one-year anniversary of the RNC’s controversial 2012 “autopsy” report that said the party “must embrace and champion comprehensive immigration reform.”

“What you have to recognize, which is an absolute truth, is that there is consensus with the Republican caucus that serious immigration reform has to happen,” Priebus said.

The comments may raise concerns about proposals to grant amnesty to millions of illegal immigrants, which have often come under the banner of “comprehensive immigration reform.” But in an interview with Breitbart News in early February, Priebus expanded on the topic and said that a broad bill on the topic didn’t have to include amnesty.

“When someone says things like, ‘we need something big.’ It doesn’t mean they’re talking about amnesty. It means border security, it means enforcement, it means legal immigration, it means E-Verify, it means a lot of things. It means guest worker programs on the border. These are all things that are accepted within the platform of the Republican party,” Priebus said then.

“I can tell you what it means for me is no amnesty whatsoever. And I’ve never been in favor of programs that are akin to amnesty. I think sanctuary cities should be cut off from federal funding, I think we ought to secure our border. I think Congress ought to follow through on its promise in 2006 on building the border fence,” he added.

GOP officials backing amnesty can often be slippery with their rhetoric, and top immigration hawks argue that providing “legal status,” as the House GOP leadership’s “principles” propose, would enable illegal immigrants to easily obtain citizenship within a few years.

Sen. Jeff Sessions (R-AL) and others have also noted that an influx of new workers, either through amnesty or increased illegal immigration, would depress the wages of American workers. For example, the Congressional Budget Office estimated the Senate “Gang of Eight” bill would lower wages for American workers and increase the unemployment rate while failing to stop future illegal immigration.

Last week, Sen. Jeff Sessions (R-AL) said embracing amnesty was precisely the wrong approach for the GOP to take after the party got walloped by low-income voters in the 2012 presidential election, and in a country in which two major polls have found that a plurality of Americans are less likely to vote for candidates who support amnesty.

“And what did the GOP’s brilliant consultant class conclude from this resounding defeat?” Sessions asked. “They declared that the GOP must embrace amnesty. The Republican National Committee dutifully issued a report calling for a ‘comprehensive immigration reform’ that would inevitably increase the flow of low-skilled immigration, reducing the wages and living standards of the very voters whose trust the GOP had lost.”

Sessions said Republicans, by opposing amnesty, could make a “clean public break from the special-interest immigration lobby” and let “Democrats own — solely, completely, and exclusively — the unwise and unpopular policies they are pushing on these groups’ behalf.”

“Isn’t it time we made President Obama, Harry Reid, Nancy Pelosi, and each of their rank-and-file members defend their near-unanimous embrace of an immigration plan that is so contrary to the wishes and interests of the American people?” he said.